Excess death rate (EDR)
The excess death rate for a group of persons of a given age
is the difference between the group's death rate and that of a suitable reference
group. For example, the mortality rate for U.S. males at age 40 is 0.00316, or 3.16
deaths per thousand person-years (Table 1). If a study shows that the mortality rate
for 40-year-old U.S. males who have some chronic disease X is 7.48 per thousand person-years,
then the EDR for condition X is 7.48 - 3.16 = 4.32 per thousand.
Expected present value (EPV)
Future payments are generally discounted: a dollar to be paid
in the future is worth less than a dollar at present. That is, the present value of
$1,000 per year for 50 years is worth less than $50,000 today. Suppose that a man's
life expectancy at his current age is 50 additional years, and that he is
promised annual payments of $1,000 for as long as he shall live. He may ultimately
receive more or less than $50,000, but on average will receive $50,000 over his life
span. But, the present value of his total -- again, on average -- will be less than
$50,000. This latter amount is known as the expected present value. See the separate
section on discounted cost of future care and expenses.
The life expectancy of a cohort of a given age is the arithmetic
mean of the actual survival times of all the individuals. For example, consider a cohort
of just five individuals all born on the same day. If they live 10, 20, 50, 60, and 80 years,
respectively, the life expectancy of the cohort is (10+20+50+60+80)/5 = 44 years. Note
that three of the individuals lived to age 40 and beyond; at age 40 their life expectancy
would be (10 + 20 + 40)/3 = 23.3 additional years.
Median survival time
The median survival time is the middle survival time for the cohort
if the survival times of are arranged from smallest to largest. For example, consider a
cohort of just five individuals all born on the same day. If the 5 individuals lived for
10, 20, 50, 60, and 80 years, respectively, then the median survival time would be 50 years.
The survivors at age 40 have medial survival time of 20 additional years. In Table 1 the
median survival time for the cohort of 100,000 individuals at birth is between 75 and 76
years, the time at which l(x) has diminished from 100,000 to 50,000. Compare to the
life expectancy of the entire cohort, 71.8 years.
The mortality rate for a cohort during a given time interval is
the number of deaths occurring during the interval divided by the total exposure, or
person-time at risk, during that interval. For example, consider a cohort of 5 individuals
followed for one year. If one person died three months into the year (one-fourth of a
person-year at risk of death), two people died six months into the year, and the remaining
two people lived to the end of the year, then the total exposure for the year is 1/4 +
2(1/2) + 2(1) = 3.25 person-years. The total number of deaths is 3. The mortality rate
is m = 3/3.25 = 0.923. The general formula for the mortality rate at age x in a life
table is m(x) = d(x)/L(x).
Mortality risk (or mortality probability)
The mortality risk for a cohort over a given time interval is the
number of people dying in the interval divided by the number alive at the beginning of
the interval. For a given age in a life table, this is q(x) = d(x)/l(x).
The multiplier is the expected present value (for a given
discount rate) of a stream of payments of 1 unit per year for the rest of an individual's
survival time. See the separate section on discounted cost of future care and expenses.
Relative risk (RR)
The relative risk of death for group A relative to group B is the
ratio of the mortality risks. Strictly this refers to the ratio of the mortality rates (m),
but it is approximately equal to the ratio of the mortality probabilities (q).
The survival time of an individual is the actual number of years
they survive beyond a given age or point in time.